The first lawsuit was filed Tuesday against the helicopter and charter companies involved in Sunday’s deadly crash in the East River — with the family of one of the victims accusing them of negligence and “carelessness.”

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It was filed in Manhattan Supreme Court by the parents of Trevor Cadigan, a 26-year-old Dallas native who lived in the Financial District.

The young man was one of five passengers on board the 2013 Eurocopter AS350 B2 when it crashed into the East River on Sunday night — killing everyone but Vance.

The helicopter was chartered by a local company called FlyNYON and owned by Liberty Helicopters, which is based out of New Jersey.

The Cadigans are seeking punitive damages from the companies, as well as Vance, for a number of things — including failure to provide “proper and safe aircraft and aircraft services,” causing or authorizing the operation of a helicopter in a “careless or reckless” manner and failure to use “ordinary care in piloting.”

They claim that Vance “failed to properly perform emergency procedures” and was “negligent and careless in failing to take reasonable steps to extricate the passengers” from the helicopter after he “secured his own release.”

They also allege that FlyNYON had a duty to their son to “exercise the highest degree of care and diligence in the operation, management, maintenance, and service of its helicopter sightseeing tours” — and ultimately caused his death due to their “failure” to do so.

Furthermore, Liberty Helicopters is “vicariously liable for any and all actions of [Vance] as to his negligent and careless piloting and operation of the subject,” the couple claims.

“The aforesaid acts and omissions on the part of the aforesaid Defendants, constitute malice, oppression, and a conscious disregard of known safety procedures and regulations,” their suit says, “thereby entitling [the Cadigans] to Punitive Damages against said Defendants, in an amount to be proven at trial.”

The family’s lawyer, Gary C. Robb, of Kansas City, Missouri, recently won a $100 million cash settlement on behalf of a passenger who was severely burned in a crash — and claims to hold the record for highest jury verdict in history for a helicopter crash, at $350 million.

Robb says he hopes the Cadigan lawsuit will prompt FlyNYON, Liberty Helicopters and other charter companies in both NYC and elsewhere to put an end to open-door flights.

“The family is simply shocked and outraged that their son drowned to death in this manner in what was supposed to be a pleasurable sightseeing helicopter tour,” Robb said, noting how there was “no prospect of his safely evacuating the helicopter in that crash scenario.”

“If this had been a normal closed-door flight with normal safety belts, it would have been so easy for Trevor to have unbuckled himself and for him to swim to the surface,” the attorney explained. “It was truly a death trap for him to be hanging upside down in frigid water temperature tightly harnessed with the release inaccessible in the back and no advance training.”

Robb added, “The family wants this helicopter operator to be held fully accountable for their son’s death and to cease and desist this terribly unsafe open-door flight operation. It is their strongest desire that this should never happen again.”